Trim the tops and bottoms of the radishes and discard. Wash the radishes and then pat dry. Slice each radish in half lengthwise and then set aside.
Sautée the shallots untill they start to brown slighlty
Add the radishes, placing each one cut side down in the skillet. Cook them undisturbed for about 2 minutes, just until the bottoms start to turn color.
Add the balsamic vinegar and then add just enough water to come up around the sides of the radishes. Cover with lid, lower the heat and simmer for 10 minutes or so.
Uncover the skillet and increase the heat to medium for a few minutes, just until the water has reduced into a syrupy sauce.
Add the parsley and toss to wilt. Season with salt and pepper to taste.